trim(Arrangement) -- make a simple hyperplane arrangement

Synopsis

• Function: trim

• Usage:

  trim A

• Inputs:
  • A, a hyperplane arrangement,
• Optional inputs:
  • Strategy => ..., default value null,
• Outputs:
  • a hyperplane arrangement, a simple arrangement

Description

i1 : R = QQ[x, y];

i2 : A = arrangement{x,x,0_R,y,y,y,x+y,x+y,x+y,x+y,x+y}

o2 = {x, x, 0, y, y, y, x + y, x + y, x + y, x + y, x + y}

o2 : Hyperplane Arrangement 

i3 : A' = trim A

o3 = {x + y, y, x}

o3 : Hyperplane Arrangement 

i4 : assert(ring A' === R)

i5 : assert(trim A' == A')

i6 : assert(trim A' == A')

i7 : A'' = restriction(A, y)

o7 = {x, x, x, x, x, x, x}

o7 : Hyperplane Arrangement 

i8 : trim A''

o8 = {x}

o8 : Hyperplane Arrangement 

i9 : A''' = dual arrangement{x, y, x-y}

o9 = {-x , x , x }
        1   1   1

o9 : Hyperplane Arrangement 

i10 : trim A'''

o10 = {x }
        1

o10 : Hyperplane Arrangement 

See also

• compress(Arrangement) -- extract nonzero equations
• prune(Arrangement) -- makes a new hyperplane arrangement in a polynomial ring
• restriction(Arrangement,RingElement) -- construct the restriction a hyperplane arrangement to a subspace
• dual(CentralArrangement) -- the Gale dual of an arrangement